Summary: The purpose of this research is to examine the effect of polarization for the problem of pure azimuthal shear of an elastic dielectric material. The present problem is investigated in context of finite deformation theory. In this paper, the author studied the effect of polarization on the stresses for Neoprene rubber and compare the results with elastic material (Mooney-Rivlin material) graphically. Twisting of a rigid cylinder in an infinite elastic medium is considered as a special case in this research.